Continuous Semi-flow With Complex Topology And Its Associated Dynamical Properties

In this paper ,we mainly study the equicontinuous and scattering properties of the continuous semi-flow on a compact metric space ,and get the results as follows :(1) the complexity function defined by spanning set is bounded if and only if the system is equicontinuous ;(2) if the continuous semi-flow is topologically weak mixing ,then it is pointwise scattering ;(3) we give several equivalent conditions that the time-one map of a continuous semi-flow is scattering. Finally ,for the minimal continuous map ,we show that the requirement of "no-dense" in the definition of scattering using open covers is not necessary.